Waveguides have numerous applications in the field of optical signal processing, and optical signal processing is often accomplished through interactions of optical waves at different frequencies mediated by a plurality of nonlinear-optic tensor coefficients of a crystal. In some materials, of which uniaxial crystal lithium niobate is an example, a strongest (highest-magnitude) tensor coefficient of “d33” requires that each of two input optical waves and a generated optical wave is polarized along a direction defined by an axis of the crystal.
However, refractive indexes of such crystals are dependent on wavelength. In one example, each of the two input optical waves and the generated optical wave include discrete wavelengths. Therefore each of the waves includes discrete refractive indices, and hence propagate at discrete velocities with respect to each other. As the waves propagate, phase fronts associated with each wave become separated from each other (a phenomenon called walk-off, or phase-mismatch), and incremental changes in amplitude of each of the waves that are incurred in any sub-section of propagation (in terms of distance through the crystal) do not add up cumulatively with changes from earlier or subsequent sections. Consequently, over any significant distance of propagation, power levels of the input optical waves do not change significantly and output power in the generated optical wave is weak relative to the power levels of the input optical waves. Such phase-mismatched operation is undesirable for nonlinear optics.
Various techniques have been used to achieve phase-matching in crystals and waveguides. Among the techniques, quasi-phase-matching (QPM) is widely used, where poling orientation of a nonlinear crystal is periodically reversed along a direction of propagation. The poling may include a spatial periodicity L selected such that 2 π/L is equal to the phase-mismatch (modulo integer multiples of 2π). Compensating for the phase mismatch (through QPM or other techniques) results in power of the generated optical wave growing cumulatively with propagation distance. Compared to the phase-mismatched case, output power may be higher in this phase-matched example by several orders of magnitude. However, a poled crystalline material may have a reduced nonlinear coefficient(s) compared to the unpatterned version of the same material.
Quasi Phase Matching (QPM) is often accomplished by reversing polarization of nonlinear coefficients periodically in the nonlinear material. Periodically-poled lithium niobate (PPLN) is Lithium Niobate that has been quasi-phase matched. However, the poling process increases fabrication complexity, and thus fabrication of quasi-phase-matched waveguides by periodically poling crystals such as Lithium Niobate and Lithium Tantalate may be challenging and not be amenable to widely-used fabrication techniques. In addition, the fabrication technique of diffusion may not allow for fine features such as: gradations in the pitch of the QPM period to accurately extend, confine and/or shape the range of wavelengths over which the nonlinear interactions occurs, or formation of interleaved or multi-periodic gratings which may simultaneously achieve QPM for multiple frequency bands.
This Background is provided to introduce a brief context for the Summary and Detailed Description that follow. This Background is not intended to be an aid in determining the scope of the claimed subject matter nor be viewed as limiting the claimed subject matter to implementations that solve any or all of the disadvantages or problems presented above.